Skip to main content

Full text of "Analytical Mechanics"

FIELDS OF FORCE AND NEWTONIAN POTENTIAL    2]
ds
Similarly
and
Hx=-
67

(D
Therefore the component, along any direction, of the intensi at any point equals the rate at which the potential diminish at that point as one moves along the given direction.
ILLUSTRATIVE EXAMPLES.
1. Find the expressions for potential and intensity at a point due to a spherical shell.
Let P, Fig. 107, be the point and R its distance from the center of the shell. Then taking a zone for the element of mass, as shown in the figure, we get
dm = <r*2irasin6 • add,
FIG. 107.
and
Therefore
r = V(R - a cos 0)2 + a2 sin20
rm dm
= -7(
sin 9 dB
-2aR cos 6
r 2ira i R     '
JK
- (a2- 2 aR + #»
There are two different cases which have to be considered separately.